The use of a potter's wheel to make pottery is one of the oldest uses of the wheel, perhaps predating use of the wheel for transportation. The pottery wheel as used today is very similar to that used in ancient times and consists essentially of a circular wheel head with a planar upper surface which is centrally mounted on a vertical shaft. The wheel head is rotated, either manually or with a motor driven system, about a central axis of rotation coaxial with the vertical shaft. A mass of wet clay is mounted at a central position on the potter's wheel and is shaped or "thrown" by manually manipulating the clay as the potter's wheel rotates. Sidewalls of a pottery vessel are created by this manipulation and are essentially completed during the throwing process. However, the bottom or "foot" of the pot cannot be finished during the throwing process. A pot is wet and very delicate after being thrown, and must be allowed to dry partially to a state known as "leather hard" before the bottom can be finished or "trimmed". During trimming, the pot is mounted upside down on the potter's wheel and held in position while the wheel turns and a trimming tool is pressed against it to cut the foot. During this trimming process, the clay is no longer wet and sticky and therefore recentering and retaining the inverted pot on the potter's wheel is very difficult. The traditional solution for retaining the pot on the potter's wheel is to place the pot in an inverted and centered position on the potter's wheel and then to place soft clay around the pot to hold it in position on the wheel. This has been a poor solution in that the holding clay, when too wet, sticks to the pot and recessitate an additional cleaning process after trimming. However, if the holding clay is too dry, the pot will not be retained on the wheel and may fly off and break while being trimmed. The very act of centering the pot by hand is very difficult, requiring both persistence and talent. An apparatus for both centering and holding a pot on a potter's wheel during trimming is the subject of my U.S. Pat. No. 4,222,577 issued Sept. 16, 1980, which is hereby incorporated by reference for all that it contains. However, although the device described in my prior patent provides a means for centering a pot on a holding apparatus which is attached to the potter's wheel, it creates another problem: how to quickly and accurately attach the centering and holding device in a centered position relative to the potter's wheel head. If the centering and holding device is itself not properly centered on the potter's wheel, then any pot held by it will rotate eccentrically, causing an annoying wobble and, if the eccentricity is sufficiently large, preventing the pot from being accurately trimmed. It is thus desirable to provide centering apparatus for accurately centering the pot centering and holding apparatus on the potter's wheel head.